Could I animate this?

Hello! I was wondering if there was a way to animate two separate objects that look the same but are rigged differently. To go into detail, I’m trying to rig a cartoon mouth. The mouth can appear on either side of the face. I can’t just stretch it from side to side because it would look horribly distorted. So, I thought I could create two separate mouths, one for each side of the face. I’m curious if it’s possible to hide one of the mouths while the other is in use, and vice versa, and keyframe them, etc.